Hopf Fibration

The Hopf fibration is a remarkable mathematical concept describing how a 3D sphere (S³) can be broken down into linked circles (called fibers), each of which is a circle. Imagine wrapping a complex network of loops inside a higher-dimensional sphere so that every point on a 2D sphere (S²) corresponds to one such loop. This creates a beautiful structure where the 3D sphere is fibers of linked circles arranged in a pattern, revealing deep connections between geometry and topology. It helps us understand complex spaces by visualizing them as intertwined routines of simpler shapes.